The Censored Normal Distribution

Description

Density, distribution function, quantile function, and random generation for the left and/or right censored normal distribution.

Usage

dcnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)

pcnorm(q, mean = 0, sd = 1, left = -Inf, right = Inf, 
  lower.tail = TRUE, log.p = FALSE)

qcnorm(p, mean = 0, sd = 1, left = -Inf, right = Inf,
  lower.tail = TRUE, log.p = FALSE)

rcnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
mean	vector of means.
sd	vector of standard deviations.
left	left censoring point.
right	right censoring point.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].

Details

If mean or sd are not specified they assume the default values of 0 and 1, respectively. left and right have the defaults -Inf and Inf respectively.

The censored normal distribution has density $f(x)$:

$\mathrm{\Phi }((left-\mu )/\sigma )$	if $x\le left$
$1-\mathrm{\Phi }((right-\mu )/\sigma )$	if $x\ge right$
$\varphi ((x-\mu )/\sigma )/\sigma$	if

where $\mathrm{\Phi }$ and $\varphi$ are the cumulative distribution function and probability density function of the standard normal distribution respectively, $\mu$ is the mean of the distribution, and $\sigma$ the standard deviation.

Value

dcnorm gives the density, pcnorm gives the distribution function, qcnorm gives the quantile function, and rcnorm generates random deviates.

See Also

dnorm